Illustrative Mathematics - Geometry - Unit 6 - Lesson 17

The 3 lines x=3,y-2.5=-\frac{1}{5}(x-0.5), and y-2.5=x-3.5 intersect at point P. Find the coordinates of P. Verify algebraically that the lines all intersect at P.

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G.GPE.4

G.GPE.5

G.CO.10

G.CO.12

Triangle ABC has vertices at (0,0),(5,5), and (10,1),. Kiran calculates the point of intersection of the medians using the following steps:Draw the triangle.Calculate the midpoint of each side.Draw the medians.Write an equation for 2 of the medians.Solve the system of equations.Use Kiran’s method to calculate the point of intersection of the medians.

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G.GPE.4

G.GPE.5

G.CO.10

G.CO.12

Triangle ABC and its medians are shown.  Write an equation for median AE.

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G.GPE.4

G.GPE.5

G.CO.10

G.CO.12

Given A=(1,2) and B=(7,14), find the point that partitions segment AB in a 2:1 ratio.

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G.GPE.4

G.GPE.5

G.CO.10

G.CO.12

A quadrilateral has vertices A=(0,0),B=(4,6),C=(0,12) and D=(-4,6). Mai thinks the quadrilateral is a rhombus and Elena thinks the quadrilateral is a square. Do you agree with either of them? Show or explain your reasoning.

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G.GPE.4

G.GPE.5

G.CO.10

G.CO.12

The image shows a graph of the parabola with focus (-3,-2) and directrix y=2, and the line given by y=-3. Find and verify the points where the parabola and the line intersect.

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G.GPE.4

G.GPE.5

G.CO.10

G.CO.12

Parabola A and parabola B both have the line y=-2 as the directrix. Parabola A has its focus at (3,4) and parabola B has its focus at (5,0). Select all true statements.

• Parabola A is wider than parabola B.
• Parabola B is wider than parabola A.
• The parabolas have the same line of symmetry.
• The line of symmetry of parabola A is to the right of that of parabola B.
• The line of symmetry of parabola B is to the right of that of parabola A.

Tags

G.GPE.4

G.GPE.5

G.CO.10

G.CO.12